Select the correct answer.
What is the value of this expression when [tex]m=6$[/tex]?
[tex]-4 \sqrt[3]{-6 m^2}$[/tex]
A. -24
B. 24
C. -144
D. 144
Answer (2)
Substitute m = 6 into the expression: − 4 3 − 6 ( 6 ) 2 .
Simplify inside the cube root: − 4 3 − 6 ( 36 ) = − 4 3 − 216 .
Calculate the cube root: − 4 ( − 6 ) .
Multiply to get the final answer: 24 .
Explanation
Substitute the value of m First, we need to substitute the value of m into the expression. We are given that m = 6 , so we replace m with 6 in the expression − 4 3 − 6 m 2 . This gives us: − 4 3 − 6 ( 6 ) 2 .
Simplify the expression Next, we simplify the expression inside the cube root. We have 6 2 = 36 , so the expression becomes: − 4 3 − 6 ( 36 ) Now, we multiply − 6 by 36 : − 6 × 36 = − 216 So the expression is now: − 4 3 − 216
Calculate the cube root Now, we need to find the cube root of − 216 . We are looking for a number that, when multiplied by itself three times, equals − 216 . Since ( − 6 ) × ( − 6 ) × ( − 6 ) = − 216 , the cube root of − 216 is − 6 . Therefore, the expression becomes: − 4 ( − 6 )
Multiply to get the final answer Finally, we multiply − 4 by − 6 : − 4 × ( − 6 ) = 24 So, the value of the expression when m = 6 is 24 .
Examples
Understanding algebraic expressions and their evaluation is crucial in various fields. For instance, in physics, you might use such expressions to calculate the potential energy of a system. Imagine a scenario where the potential energy U depends on a variable x as U = − 5 3 − 2 x 2 . If x = 3 , you would evaluate the expression to find the potential energy: U = − 5 3 − 2 ( 3 ) 2 = − 5 3 − 18 . This calculation helps determine the stability and behavior of the system. Similarly, in engineering, evaluating expressions is essential for designing structures and predicting their performance under different conditions.
The value of the expression − 4 3 − 6 m 2 when m = 6 is 24 . The correct answer is option B: 24.
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